Modeling Paid and Incurred Losses Together

The modeling skills of actuaries and academicians have developed to the point of their seeking joint models for paid and incurred losses, i.e., models in which paid and incurred losses will inform each other so that their confidence intervals will narrow and the two sets of ultimate losses will be equal. The key to such models is covariance; heteroskedastic models cannot serve the purpose. Properly accounting for covariance in the linear statistical model will provide an exact, sound, and elegant solution to the problem. Moreover, covariance is what distinguishes the same information from like information, and prevents the creation of information out of nothing.

Key concepts: linear statistical model, paid and incurred losses, seemingly unrelated regression (SUR), covariance, variance structure